STA 220F: Statistics

University of Toronto at Mississauga, Summer 2004

Lecture: Monday and Wednesday 1:10-3:00 p.m., Room 292, North Building (Room 205 North Building on May 26th only)

Tutorials:

• MW 11:10 am - 12:00 pm, Room 144 North Building
• MW 12:10 pm -  1:00 pm, Room 144 North Building
• MW  3:10 pm -  4:00 pm, Room 292 North Building (Room 205 North Building on May 26th only)

This page is under construction, and will be updated frequently throughout the course.

Quiz 5 Solutions and problems are posted.

Final Exam Schedule is official. Our exam is Monday at 2.

Final Formula Sheet is available.

Look at the Hints on the Final Exam

Office Hours for the Final Exam

• Friday June 25th
  • Christine in 3093H, 10am - 12 noon
  • Jerry in 4059C, 12 noon - 2pm
• Monday June 28th: Jerry in 4059c, 10am - 12 noon

• About the Final Exam
• Final Exam Schedule
• Quiz Marks
• Solutions to Quizzes 2 and 3
• Solutions to Quiz 4
• Quiz 5 questions
• Solutions to Quiz 5
• Course Outline
• Christine's Minitab Handout
• Email from students, with responses. Last updated June 22nd.
• Final Formula Sheet: Will be provided with Final Exam.
• Probability Handout: Replaces Chapter 3 and most of 4.
• Assignments
  1. Read Chapter One and do Problems 1.2, 1.5, 1.6, 1.7, 1.11, 1.12, 1.13, 1.15-1.19, 1.22, 1.27.

     Read Chapter 2, skipping Sections 2.6 and 2.8. In section 2.7, any references to "Cheshev's Rule" and the "Empirical Rule" can be ignored; they are based on Section 2.6, for which you are not responsible. You are not officially responsible for Section 2.10 (how to lie with statistics), but please read it for entertanment and general education. Do problems 2.1, 2.2, 2.3, 2.6, 2.12, 2.16, 2.18, 2.19, 2.20, 2.22, 2.27, 2.33, 2.34, 2.35, 2.37, 2.38, 2.39, 2.40, 2.41, 2.42, 2.43, 2.54-2.57, 2.59, 2.60, 2.61, 2.65, 2.82, 2.87, 2.108, 2.109

     Do all this in preparation for Quiz One on Wednesday, May 26th. The problems are not to be handed in. They are just preparation for the quiz.

      

  2. Read the Probability handout, and do problems 3.1, 3.3, 3.4, 3.10, 3.11, 3.13, 4.6, 4.7, 4.8, 4.9, 4.10, 4.11, 4.12, 4.13, 4.17.

     Now read the discussion of discrete and continuous random variables on pages 174-176 in Chapter 4. Then read Chapter 5's Introduction and Section 5.1. Skip Section 5.2, but read 5.3 carefully. Do problems 5.16, 5.17, 5.18, 5.19, 5.21, 5.22, 5.23, 5.24, 5.28, 5.29, 5.32, 5.33, 5.34, 5.35, 5.36, 5.37.

     Do this in preparation for Quiz Two on Wednesday, June 2nd. The problems are not to be handed in. They are just preparation for the quiz.

      

  3. Read Section 6.1, skip Section 6.2 and read Section 6.3. Do problems 6.15, 6.16, 6.19, 6.20, 6.24, 6.25, 6.28, 6.46. Recall from lecture that if the distribution of scores in the population is normal, the sampling distribution of the sample mean is also normal, regardless of the sample size. Then do the Supplemental Problems.

     Read Section 7.1. Do problems 7.1, 7.2, 7.3, 7.4, 7.5, 7.11, 7.12, 7.15, 7.18.

     Do this in preparation for Quiz Three on Wednesday, June 9th. The problems are not to be handed in. They are just preparation for the quiz.

      

  4. Start with problems 7.6 and 7.14. I know for 7.14 the sample size is exactly 30, but otherwise it is a good enough problem. Then read Section 7.2 and do Problems 7.23, 7.25, 7.27, 7.29, and 7.33. In Questions 7.27 and 7.29, what piece of information did the authors forget to supply?

     Read Section 7.3 and do problems 7.37, 7.39, 7.40, 7.41, 7.42, 7.45, and 7.46. Skip Section 7.4 on determining sample size.

     Read Sections 8.1 and 8.2. Do Problems 8.4, 8.5, 8.7 through 8.14, and 8.18 through 18.21. For any homework question that asks for the null hypothesis, please give 4 answers:

     1. Null Hypothesis in words
     2. Null Hypothesis in symbols
     3. Alternative Hypothesis in words
     4. Alternative Hypothesis in symbols
     This is the way you will be asked for it on the Quiz and the Final.

     Do this in preparation for Quiz Four on Wednesday, June 16th. As usual, the problems are not to be handed in. They are just preparation for the quiz.

      

  5. For this assignment, whenever you encounter a word problem asking for a hypothesis test, the following questions are more important than the question in the book. If the book is asking something that goes beyond these questions, answer that too.
     1. State the null hypothesis
        1. In words.
        2. In symbols.
     2. State the alternative hypothesis
        1. In words.
        2. In symbols.
     3. Give the rejection region for alpha=0.05 (or alpha=0.01).
     4. Give the numerical value of the test statistic. The answer is a number. Show your work.
     5. Do you reject H₀? Answer Yes or No.
     6. Give the p-value. The answer may be a range of numbers.
     7. State your conclusion
        1. In words.
        2. In symbols.

     Note that in class, my null hypotheses for one-tailed tests are always of the form µ<µ₀ or µ>µ₀, but the book sometimes (not always) states it as H₀:  µ=µ₀, especially in problem solutions. We will give full marks for the book's style of stating the null hypothesis.

     First, do the Computer Assignment. Then do problem 8.21 (again), 8.23, 8.24, 8.29 (be sure to do b and c), read Section 8.3, do problems 8.31, 8.32, 8.36, 8.43, Read Section 8.4, do 8.45 (our answer is different from the book's), 8.53, 8.58, Read Section 8.5, do 8.61, 8.66, 8.73. Skip Sections 8.6 and 8.7.

     Do problems from the book in preparation for Quiz Five on Wednesday, June 23d. The problems are not to be handed in. They are just preparation for the quiz. But remember to bring your printouts from the computer part, with nothing written on them except possibly your name and student number.

      

  6. For all the assigned problems, be able to answer the standard questions about hypothesis tests. That is,
     1. State the null hypothesis
        1. In words.
        2. In symbols.
     2. State the alternative hypothesis
        1. In words.
        2. In symbols.
     3. Give the rejection region for alpha=0.05 (or alpha=0.01).
     4. Give the numerical value of the test statistic. The answer is a number. Show your work.
     5. Do you reject H₀? Answer Yes or No.
     6. Give the p-value. The answer may be a range of numbers.
     7. State your conclusion
        1. In words.
        2. In symbols.

     Read Section 9.1. Don't worry about confidence intervals for a difference between population means. It will not be on the final. When you read about the t-test for "small samples," remember that it applies to large samples too, provided the distribution in each population is normal, with equal variances. You can ignore the t-test that does not assume equal variances.

     Do the hypothesis test part of Example 9.4 with Minitab; assume equal variances. Try to get the exact p-value.

     Do 9.11, 9.13 (use Minitab), 9.18 (normal assumption is probably okay). Why is it unrealistic to assume a normal distribution for the data of problem 9.19?

     Read section 9.2, but realize that the paired t-test is just a one-sample t-test conducted on differences. The authors do us a dis-service by giving separate formulas. The examples are okay, though.

     Do example 9.5 with Mintab. Do problem 9.38.

     Read Section 9.3. Do example 9.6 with Minitab. Do problem 9.57, with and without Minitab.

     Read Sections 13.1, 13.2 and 13.3. Do problems 3.11, 3.12, Ex. 13.3 with Minitab, 13.22 with Minitab. When you are answering the standard questions while applying the chisquare test of independence, don't try to state null, alternative and conclusions in symbols; just use words.

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